### Abstract

We evaluate, by means of variational calculations, the bound state energy EB of a pair of charges located on the surface of a cylinder, interacting via Coulomb potential - e^{2}/^{r}. The trial wave function involves three variational parameters. EB is obtained as a function of the reduced curvature C=a_{0}/R, where a_{0} is the Bohr radius and R is the radius of the cylinder. We find that the energetics of binding exhibits a monotonic trend as a function of C; the known one- and two-dimensional limits of EB are reproduced accurately by our calculation. E_{B} is relatively insensitive to curvature for small C. Its value is ∼1% higher at C = 1 than at C = 0. This weak dependence is confirmed by a perturbation theory calculation. The high curvature regime approximates the one-dimensional Coulomb model; within our variational approach, E_{B} has a logarithmic divergence as R approaches zero. The proposed variational method is applied to the case of donors in single-wall carbon nanotubes.

Original language | English (US) |
---|---|

Article number | 075407 |

Pages (from-to) | 754071-754075 |

Number of pages | 5 |

Journal | Physical Review B - Condensed Matter and Materials Physics |

Volume | 66 |

Issue number | 7 |

DOIs | |

State | Published - Aug 15 2002 |

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### All Science Journal Classification (ASJC) codes

- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics

### Cite this

*Physical Review B - Condensed Matter and Materials Physics*,

*66*(7), 754071-754075. [075407]. https://doi.org/10.1103/PhysRevB.66.075407

}

*Physical Review B - Condensed Matter and Materials Physics*, vol. 66, no. 7, 075407, pp. 754071-754075. https://doi.org/10.1103/PhysRevB.66.075407

**Variational approach to the Coulomb problem on a cylinder.** / Kostov, M. K.; Cole, Milton Walter; Mahan, G. D.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Variational approach to the Coulomb problem on a cylinder

AU - Kostov, M. K.

AU - Cole, Milton Walter

AU - Mahan, G. D.

PY - 2002/8/15

Y1 - 2002/8/15

N2 - We evaluate, by means of variational calculations, the bound state energy EB of a pair of charges located on the surface of a cylinder, interacting via Coulomb potential - e2/r. The trial wave function involves three variational parameters. EB is obtained as a function of the reduced curvature C=a0/R, where a0 is the Bohr radius and R is the radius of the cylinder. We find that the energetics of binding exhibits a monotonic trend as a function of C; the known one- and two-dimensional limits of EB are reproduced accurately by our calculation. EB is relatively insensitive to curvature for small C. Its value is ∼1% higher at C = 1 than at C = 0. This weak dependence is confirmed by a perturbation theory calculation. The high curvature regime approximates the one-dimensional Coulomb model; within our variational approach, EB has a logarithmic divergence as R approaches zero. The proposed variational method is applied to the case of donors in single-wall carbon nanotubes.

AB - We evaluate, by means of variational calculations, the bound state energy EB of a pair of charges located on the surface of a cylinder, interacting via Coulomb potential - e2/r. The trial wave function involves three variational parameters. EB is obtained as a function of the reduced curvature C=a0/R, where a0 is the Bohr radius and R is the radius of the cylinder. We find that the energetics of binding exhibits a monotonic trend as a function of C; the known one- and two-dimensional limits of EB are reproduced accurately by our calculation. EB is relatively insensitive to curvature for small C. Its value is ∼1% higher at C = 1 than at C = 0. This weak dependence is confirmed by a perturbation theory calculation. The high curvature regime approximates the one-dimensional Coulomb model; within our variational approach, EB has a logarithmic divergence as R approaches zero. The proposed variational method is applied to the case of donors in single-wall carbon nanotubes.

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U2 - 10.1103/PhysRevB.66.075407

DO - 10.1103/PhysRevB.66.075407

M3 - Article

VL - 66

SP - 754071

EP - 754075

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 1098-0121

IS - 7

M1 - 075407

ER -